Official Guide Explanation:
Problem Solving #151

Background

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Solution and Metadata

Question: 151
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Counting Methods > Combinations

Explanation: This is a combinations question. There are 7 possible selections of 1 person from a group of 7 candidates for the math position. The number of selections for the computer science positions is trickier. To find the number of possibilities of 2 selections from 10 candidates, use the combinations formula:

c = ((n!)/(k!(n - k)!)) = ((10!)/(2!8!)) = ((10(9))/2) = 45

Since there are 7 possibilities for the math position and 45 for the comp sci positions, the total number of sets is the product:

7(45) = 315, choice (E).

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